Systems, methods and computer-implemented architectures for performing supply chain planning

ABSTRACT

Methods, systems and computer-implemented architectures are provided for performing supply chain planning. In one implementation, a system is provided that comprises a database configured to store master data descriptive of supply chain items, a model generator coupled to the database and configured to derive a master data-based core model representative of a supply chain planning problem, and a solver configured to translate the core model into a mathematical model and determine a solution to the mathematical model. In addition, the system may comprise a preprocessor configured to preprocess the core model by subjecting the core model to a set of rules to derive a preprocessed core model, wherein the solver establishes the mathematical model from the preprocessed core model. By applying a set of preprocessing rules to the core model, where the business logic of the supply chain planning problem still exists, the solving process of the planning problem can be improved and the performance of the solver can be enhanced. Moreover, meaningful results obtained from the preprocessing can be reported to a customer.

TECHNICAL FIELD

The present invention generally relates to the field of data processingand computer-supported supply chain planning. More specifically, theinvention relates to methods, systems and computer-implementedarchitectures for optimizing supply chain planning problems.

BACKGROUND INFORMATION

Planning a supply chain has become a highly complex task in modernindustries. A complete supply chain may cover all supply network areasfrom a supplier's supplier to a customers customer. A complete supplychain may be modelled, for example, from master data such as locations,products, resources, bills of material, etc. and from data representingtransport relations.

A resource may be defined, for example, as referring to a machine,person, facility, warehouse, means of transportation or other asset witha limited capacity that fulfils a particular function in the supplychain. A resource's capacity may be defined, for example, by a quantity(e.g., transport or warehouse capacity) or a per-time rate (e.g.,production rate per day or week).

A location may be defined, for example, as referring to a place ororganizational entity at which quantities of products or resources aremanaged. Exemplary locations include a production plant, a distributioncenter, a transportation zone, a stock transfer point, a storagelocation area, a customer, a vendor (external supplier), asubcontractor, a transportation service provider, a terminal, ageographical area, and a store.

A product may be defined, for example, as referring to a good that isthe subject of business activity. A product can be used, consumed orcreated in the course of a production process. Thus, a product can beany of a raw product, an intermediate product and a final product. Alocation-product may then be defined by assigning a product to aspecific location in a supply chain model. Similarly, a lane-product maybe defined by assigning a product to a lane of transportation in asupply chain model.

A bill of material may be defined, for example, as referring to acomplete, structured list of the components that make up an object.

Automated supply chain solutions are available in the marketplace andprovide various features. For example, SAP AG's presently marketedsoftware solution for planning and controlling the entire supply chain,Advanced Planner and Optimizer (APO), defines production process model(PPM), operation, and activity as further master data. A productionprocess model describes when a plan can be used to manufacture aproduct. It brings together a bill of material and a work plan or tasklist and allows to determine at which production facility in whatquantity and in what manner a product can be manufactured at aparticular time. A production process model will include at least oneoperation which, in turn, will contain at least one activity. Anoperation describes an action within a PPM plan and oftentimes consistsof numerous activities. An activity thus represents a separate stepwithin an operation. For example, the operation drilling may consist ofthe following activities: setting up a drill, operating the drill, andtearing down the drill.

It is to be understood that the above-described types of master data aremerely exemplary and non-limiting. A person of ordinary skill in the artwill readily appreciate that other types of master data are conceivableas well and that the particular application may determine the types ofmaster data to be used.

Supply chain planning frequently involves different types of planningthat allow to plan and optimize different aspects of the supply chain.For example, supply network planning may allow to create a plan thatdescribes the product flow along the supply chain so that all the demandrequirements can be met. Production planning may allow the planner tocreate feasible production plans across different production locationsto fulfil a demand in time and to the standard expected by the customer.Transportation planning may allow to create a least cost transportationplan while guaranteeing customer service. Other types of planning mayexist as well and be implemented in a supply chain planning system.

Supply chain planning problems oftentimes can be formulated as finding aminimum (or maximum) value for an objective function while observing anumber of constraints. A typical objective function relates to theoverall costs of the production or transportation plan. It can be saidthat it is a general goal to keep costs as low as possible. Time canalso be the subject of an objective function (as, e.g., in the case ofhaving to find a least time consuming plan for transporting goods).Constraints can be imposed, for example, by required safety stocks, themaximum capacity of resources, time requirements, etc.

For finding a solution to a supply chain planning problem, it is acommon approach to develop a mathematical representation of the problemand solve the mathematical problem using optimization techniques. Agreat many of supply chain planning problems can be formulated by alinear objective function and linear equalities or inequalitiesrepresenting the constraints. Such problems are frequently referred toas linear programming (LP) problems. In practical scenarios, the LPrepresentation of a supply chain planning problem may easily containseveral hundred thousand variables or even more than that. If thevariables are integer variables, i.e., they can only assume integervalues such as a binary value, the problem is called an integer LPproblem. In many cases, however, a supply chain planning problem willnot only involve integer variables, but variables that may assumenon-integer values. The problem is then called a mixed integer linearprogramming (MILP) problem.

Numerous algorithms have been developed in the art for solving LPproblems, including the Simplex algorithm and branch-and-bound andbranch-and-cut algorithms for solving MILP problems. All thesealgorithms are well-known in the art and it is not necessary toelaborate thereon in detail here.

Computation time and computation resources are crucial factors inachieving a optimal solution to a supply chain planning problem.Unfortunately, LP problems and particularly MILP problems are sometimesextremely difficult to solve or even impossible to solve in reasonablecomputation times. While the number of variables involved in the problemmay have an impact on the necessary computation time, it has been foundthat even comparatively small MILP problems (small referring to thenumber of variables, for example, less than one hundred) may sometimesbe extremely hard to solve.

Usually, there exist several semantically equivalent models for a givenproblem which are not equally hard to solve. One can therefore attemptto find one of the alternatives that can be solved more easily thanother alternatives.

To keep the necessary computation time and computation resources atacceptable levels, however, techniques for preprocessing LP and MILPproblems have been developed that allow to transform a given planningproblem into one that can be solved more efficiently. Preprocessors areknown to employ two main techniques in order to achieve thepreprocessing, reformulation and simplification. Reformulation meansthat some parts of the model are modified or exchanged by others.Reformulation is based on rules. Each rule represents one preprocessingstep. By applying a rule to a model, a reformulated model is obtainedthat one hopes is simpler to solve. Simplification, on the other hand,is a technique that removes redundancy from the problem. Again,simplification relies on rules. Applying a rule results in a simplifiedmodel.

A preprocessor applies the different rules as long as they areapplicable. The resulting model represents the preprocessed model, whichis expected to require less computation time and resources to solve.

It is known to employ preprosessing techniques at the mathematicallevel, i.e., after a supply chain planning problem described in terms ofmaster data and demands has been converted to a mathematicalformulation. The following two articles highlight various techniques forpreprocessing zero-one and mixed integer linear programming problems atthe mathematical level: Preprocessing and Probing Techniques for MixedInteger Programming Problems by M. W. P. Savelsbergh, ORSA Journal onComputing, Vol. 6, No. 4, Fall 1994, pp. 445-454; and ImprovingLP-Representations of Zero-One Linear Programs for Branch-and-Cut byKarla L. Hoffman and Manfred Padberg, ORSA Journal on Computing, Vol. 3,No. 2, Spring 1991, pp. 121-134.

SUMMARY OF THE INVENTION

Consistent with embodiments of the invention, methods, systems andcomputer-implemented architectures are provided for performing supplychain planning.

According to one object, computerized methods and systems are providedto enable efficient solving of supply chain planning problems withreasonable computation time and using reasonable computation resources.

In accordance with one embodiment, a computer-implemented architectureis provided for performing supply chain planning, the architecturecomprising a database storing master data descriptive of supply chainitems, a model generator coupled to the database and configured toderive a master data-based core model representative of a supply chainplanning problem, and a solver configured to translate the core modelinto a mathematical model and determine a solution to the mathematicalmodel. The computer-implemented architecture may also include apreprocessor configured to preprocess the core model by subjecting thecore model to a set of rules to derive a preprocessed core model,wherein the solver establishes the mathematical model from thepreprocessed core model.

According to an aspect of the present invention, the preprocessor mayreceive as an input the core model, which is described on the basis ofthe master data. In other words, the preprocessor operates at a levelwhere the business logic still exists. Preprocessing the core model canimprove both the core model and, implicitly, the mathematicalformulation thereof. Translating the preprocessed core model to themathematical level then results in a mathematical model that is simplerto solve than the mathematical problem that would result from theoriginal non-preprocessed core model. In this connection, embodiments ofthe present invention envisage that the mathematical model itself can beadditionally subjected to some form of preprocessing such as described,e.g., in the above-recited articles. Such additional preprocessing atthe mathematical level, however, is a mere option and is not necessarilyrequired when solving a supply chain planning problem usingarchitectures consistent with the present invention.

Embodiments of the present invention may provide the further advantagethat the preprocessing algorithm implemented in the preprocessor can beindependent of the specific optimizer algorithm utilized in the solverfor solving the mathematical problem. It is thus conceivable to use thesame preprocessor for a variety of different supply chain planningmodules that perform different planning tasks.

Preprocessing the core model, also, has the advantage that meaningfulresults at the business level can be obtained. If preprocessing isperformed at the mathematical level, results may not necessarily beinterpretable in a meaningful way in terms of the result of thepreprocessing at the business level. Consistent with an aspect of thepresent invention, however, methods and systems may be provided thatidentify, e.g., redundant data or demands that can not be fulfilledthrough preprocessing the core model and report such results to thecustomer.

The set of rules implemented in the preprocessor may include one or moreredundancy elimination rules. In addition, or as an alternative, the setof rules may include one or more remodelling rules. Elimination ofredundancy and remodelling allows to reduce the size of the core modeland, hence, the size of the mathematical problem. Elimination ofredundancy can be achieved, e.g., by eliminating data not required forthe optimization and data where there is no degree of freedom withrespect to the planning decisions. A data object is not required for theoptimization if the optimizer solution with this object is equal to theoptimizer solution without this object with respect to the resultingplanning decisions (as in procurement, production, transport, etc.).Since the core model is more expressive than the master data basedmodel, remodelling may allow to create a simpler but equivalent model.It may also allow to create a simpler similar model if, for example, theoriginal model contains a degree of freedom that can not be avoided, butis really not required. This is based on the principle that no moredegree of freedom than required shall be included in the model.

The set of rules implemented in the preprocessor may further include oneor more big number reduction rules and one or more bound reductionrules. By reducing big numbers or variable bounds in the core model,numerical stability can be improved and the linear relaxation of theproblem can be strengthened. As the computations will be typicallyperformed using finite precision floating point arithmetic, bigdifferences in numbers may occur, which can cause badly scaled problems.Reducing the big numbers can help prevent such problems and keepdifferences between numbers small.

Additional objects and advantages of the invention will be set forth inpart in the description which follows, and in part will be obvious fromthe description, or may be learned by practice of the disclosedembodiments of the invention. The objects and advantages of theinvention will be realized and attained by means of the elements andcombinations particularly pointed out in the appended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate several embodiments of theinvention and together with the description, serve to explain theprinciples of the invention. In the drawings:

FIG. 1 is a block diagram that depicts an exemplary computer-implementedsystem architecture, consistent with an embodiment of the presentinvention, that includes a supply chain planner and optimizer module;

FIG. 2 illustrates a work flow of a method for optimizing and solving asupply chain planning problem, consistent with an embodiment of thepresent invention; and

FIGS. 3, 4, 5 and 6 illustrate exemplary scenarios for the applicationof redundancy elimination and remodelling rules, consistent withembodiments of the present invention.

DESCRIPTION OF THE EMBODIMENTS

In the exemplary computer-implemented system architecture of FIG. 1, asupply chain planner and optimizer module is designated 10 and is linkedvia an interface module 12 to an online transaction processing (OLTP)module 14. The module 10 is also linked to a data warehouse module 16,as shown in FIG. 1.

In the embodiment of FIG. 1, the OLTP module 14 can be formed of, forexample, an R/3 software system of SAP AG (Walldorf, Germany), but caninclude any other software system(s) or module(s) as well. The datawarehouse module 16 can be formed of, for example, SAP AG's BusinessWarehouse software package, but again can be formed of other softwarepackage(s) or solution(s) as well. By way of further example, theinterface module 12 can be formed of SAP AG's Core Interface (CIF)software package, although other software providing similar functionscan be used as well.

The planner and optimizer module 10 can be based on SAP AG's AdvancedPlanner and Optimizer (APO) software system. The module 10 may include adatabase 18 that contains all the data relevant for a supply chainplanning problem. This data specifically includes master data asexemplified above and also includes data related to demands, supplies,capacity profiles, etc. In one embodiment, the database 18 communicateswith the data warehouse module 16 and the OLTP module 14 to obtainup-to-date data. It can be implemented, for example, in SAP AG'sLiveCache technology.

The planner and optimizer module 10 further includes one or moreplanning modules 20 for performing various planning functions. One suchplanning function is supply network planning (SNP), which determines,based on a sales target, a short- to mid-term plan for the flow ofproducts along the entire supply chain so as to achieve the targetedsales. At least one of the planning modules 20 may perform SNP planning.For instance, in FIG. 1, this module is discriminated by an asteriskfollowing its reference number (i.e., 20*). The other planning modules20 may be concerned with planning functions such as sales planning,production planning, transport planning, global availability checkingand so forth.

Consistent with an aspect of the invention, the SNP planning module 20*includes a master data-based representation (or model) of the supplychain. Based on a user-defined selection, all master data relevant to aspecific part of the model or the entire model is extracted along withassociated transactional data. The extracted data (extracted model) iscomprised of a set of relational tables. The tables are provided to asolver module 22, which has implemented therein algorithms forgenerating an object-oriented core model from the extracted model,preprocessing the core model at the business level, translating thepreprocessed core model to the mathematical level and solving themathematical model thus obtained. The conversion of the extracted modelto the core model may take place at the business level to preserve thebusiness semantics of the model. Decoupling the model representation inthe planning module 20* and the solver 22 allows to couple differenttypes of solvers to the planning module 20*, couple the same solver 22to different planning modules, and implement the planning module 20* andthe solver 22 using different technological platforms.

The algorithms for solving the planning problem at the mathematicallevel can employ linear programming techniques, such as a Simplex orbranch-and-bound algorithm, for example. It is to be noted, however,that LP techniques and particularly MILP techniques are but one exampleof the techniques that may be used for solving mathematical models ofproblems in the field of supply chain planning and that other techniquesknown in the art can be likewise used for this purpose. Accordingly,embodiments of the present invention are not limited to LP or MILPprogramming techniques.

Referring to FIG. 2, a work flow is provided of an exemplary method forperforming supply chain planning, consistent with an embodiment of thepresent invention. The exemplary method of FIG. 2 will be described withreference to the computer-implemented architecture of FIG. 1.

As shown in FIG. 2, a model generator 24 builds an object-oriented model(core model 26) from a solver-independent, table-based planning modelusing master data items, such as location, lane, product, resource, PPM,etc., from the database 18. A preprocessor 28 receives the masterdata-based core model 26 and applies a set of preprocessing rules tocreate a preprocessed core model 30. The preprocessed core model 30 isan improved representation of the core model 26 at the same level, i.e.,the business level.

A translator 32 may then translate the preprocessed core model 30 into amathematical model 34, which is subsequently solved by an optimizer 36.In one embodiment, the translator 32 describes the mathematical model 34in terms of variables, inequalities and objective functions. Followingthe optimizer 36, a solved preprocessed core model 38 is obtained, whichmay be postprocessed by the preprocessor 28 to generate a solved coremodel 40. The solved core model 40 may subsequently be fed back to thedatabase 18 via the model generator 24. In one embodiment, the modelgenerator 24, preprocessor 28, translator 32 and optimizer 36 are allimplemented in the solver module 22. Any suitable combination ofhardware, software and/or firmware may be used for this purpose.

In a preferred embodiment, the rules applied by the preprocessor 28 forpreprocessing the core model 26 can be classified into three categories:(i) rules for eliminating redundancy, (ii) rules for improving thenumerical properties and linear relaxation, and (iii) rules forremodelling. In the following description, a more detailed explanationof exemplary rules from each of these categories will be given.

Exemplary Rules for Redundancy Elimination

The size of the problem may have a major impact on the performance ofthe optimization process in terms of storage consumption and solvingspeed. Rules for eliminating redundancy may aim at identifying andeliminating parts of the planning problem that have no influence on theresult of the optimization.

In one embodiment, a first redundancy elimination rule checks the supplychain (better: the core model) for location products and dependentobjects that can be eliminated from the core model.

Generally, an optimized plan for a supply chain planning problem may aimat planning production, transport and procurement orders such that alldemands and all safety stocks can be met under given restrictions (e.g.,finite capacities). It has been found that a planning problemoften-times involves location products as defined above for which nodemands or safety stock requirements exist. As a consequence, allelements of the supply chain necessary to meet a potential demand ofsuch a product are redundant unless these elements are at the same timenecessary to fulfil an actually existing demand for another product.

According to a first preprocessing rule, the supply chain is analyzedfor each location product. If any location products are found for whichno demands and safety stock requirements exist, these location productsare eliminated along with any dependent portions of the model which neednot be utilized (as they are not needed for meeting a demand).

FIG. 3 illustrates the first preprocessing rule by way of a simpleexample. In FIG. 3, a portion of a supply chain is illustrated whichincludes: production process models represented by a lozenge symbol,products represented by an octagon symbol, and transport lanesrepresented by an arrow. In the scenario illustrated in FIG. 3, a demandexists for a product 42 at a location L1. On the other hand, no demandexists for a product 44 at the same location L1. Accordingly, the supplychain section shown in FIG. 3 is checked whether or not the locationproduct (44, L1) (i.e., product 44 at location L1) can be eliminated. Tothis end, the supply chain section is back-propagated from the locationproduct (44, L1) to identify any supply chain items that are exclusivelyused for providing the product 44 at location L1. By so doing, it isfound that the following supply chain items solely depend on thelocation product (44, L1): a product 46 at a location L2, a product 48at a location L3 and transport lanes 50, 52 between locations L2 and L1and between locations L3 and L2, respectively. All these supply chainitems, i.e., items 44, 46, 48, 50 and 52, can be eliminated from thesupply chain section shown in FIG. 3, thus simplifying the core model tobe solved.

Furthermore, when checking the supply chain section of FIG. 3, a product54 at a location L4 will also be identified as not being required forproviding the product 42. The product 54 is output from a productionprocess model 56, which receives a product 58 as an input product. Asthe supply chain items 54, 56, 58 are not necessary to fulfil the demandwith respect to the product 42, they can also be eliminated from thesupply chain.

As demonstrated by the example of FIG. 3, the supply chain can bestreamlined by eliminating location products not required for demand orsafety stock satisfaction and also eliminating any dependent lanes,locations, lane locations and activities (such as procurement,transport, PPM).

Redundancy elimination, as discussed by the example above, is based on ademand perspective (pull). It is to be understood though that redundancycan also be eliminated in the planning problem through application of astock-related perspective (push). This means that any potential stock isanalyzed as to where it can be “pushed” in the supply chain. Anyproductions, transports and involved location products in the push routeor routes must not be eliminated.

In accordance with another embodiment, a second redundancy eliminationrule may be provided that aims to eliminate resources.

In general, resources constitute capacity restrictions. If a capacityrestriction limits a single planning decision only, it is easier for thesubsequent optimization to express this limitation in terms of a reduceddefinition range of the variable representing the planning decision. Thesecond redundancy rule may check all resources for this property andeliminate those with the property after limiting the definition range ofthe variable accordingly.

FIG. 4 illustrates example of the application of the second rule. InFIG. 4, a production process model 60 receives input products 62, 64 anddelivers output products 66, 68. In order to produce the output products66, 68, the PPM 60 utilizes resources 70, 72, which are indicated by aflattened hexagon symbol. The resources 70, 72 are exclusively utilizedby the PPM 60. No other planning decisions rely on the resources 70, 72.In this case, the capacities represented by the resources 70, 72 can bepropagated to the PPM 60 by adapting upper bounds within the PPM 60correspondingly. The resources 70, 72 can then be deleted. The modifiedPPM thus obtained is designated 60′ in FIG. 4. As can be seen, theelimination of the resources 70, 72 simplifies the model and can improvethe performance of the optimizer at the mathematical level.

Exemplary Rules for Improving Numerical Properties and Linear Relaxation

Linear programming involves the solving of a system of linear equalitiesor inequalities. Owing to the floating point arithmetic of computers,which provides a finite accuracy only, rounding or cancellation problemsmay occur during solving of the equalities or inequalities. Suchproblems are less likely to occur if the range of numbers involved inthe optimization problem is kept small. Rules may therefore be providedthat aim at reducing big numbers, provided such reduction does not alterthe set of admissible solutions.

To this end, consistent with an embodiment of the invention, a thirdpreprocessing rule may be provided that relates to the elimination ofdemands and safety stocks.

The satisfaction of a demand is a so-called soft constraint in themathematical model on which the optimization is based. This means thatthe constraint may be violated at the expense of a penalty cost in theobjective function. This may be necessary since it may not be guaranteedthat all demands or safety stocks can be met (e.g., due to a shortage incapacity). Usually, big numbers (e.g., values in the range of 10⁶-10⁸)are used as penalty cost in the objective function. It is a purpose ofthe third preprocessing rule to identify any demands or safety stocksthat can not be satisfied with certainty. In this case, the demands andthe correspondingly big penalty cost can be eliminated from theobjective function.

In accordance with another embodiment, a fourth preprocessing rule maybe implemented that is concerned with the reduction of big M numbers.

Big M modelling is a conventionally utilized technique for modellingminimal lot sizes, fixed resource consumption or fixed costs. In thetechnique of big M modelling, a variable Z, which can only assume thevalue 0 or 1, is combined with a random variable X such that Z=1 for X>0and Z=0 for X=0.

To give an example, a production process will be oftentimes considereduseless unless a certain minimal amount (minimal lot size) can beproduced. In the mathematical model, this constraint can be modelled asfollows:I·Z≦XX≦M·Zwhere X is a variable representing the produced amount, Z is anindicator variable that either assumes the value 0 or the value 1, I isa constant representative of a minimal lot size (e.g., 100), and M is abig number so defined that it does not limit X (“big M” constant).

According to the range of values for Z:Z=0:I·0≦X≦M·0→X=0Z=1:I·1≦X≦M·1→I≦X≦M

Thus, the produced amount is either zero (X=0) or corresponds to atleast the minimal lot size I (I≦X≦M).

The fourth rule aims to select the constant M as small as possible, butbig enough so as not to limit X. To this end, the rule examines otherconstraints involving the variable X to derive a maximum value for X sothat no violation of the constraints occurs. Examples for such otherconstraints are capacity restrictions of production resources ormaterial availability restrictions (e.g., stock-restricted production).

Consistent with yet another embodiment, a fifth preprocessing rule maybe provided that relates to the adaptation of lot sizes for procurement.

The procurement of raw materials is at the beginning of a supply chain.Frequently, large amounts of raw materials are present in supply chainsthat have a converging product flow. As an example, a large number ofscrews may be required for manufacturing a complex machine. In themathematical model, the corresponding variable may easily assume a veryhigh value. If, as an example, the procurement of the product is subjectto a piecewise linear cost function (such as for modelling a grading ofrebates), this will be modelled by a “big M” structure at themathematical level. For this purpose, the constant M, again, must beestimated as explained above in connection with the fourth rule. In viewof the fact that procurement values may become very large, the big Mconstant must be selected correspondingly large. This can lead tonumerical problems. The rule therefore aims at reducing the value of theprocurement variable in the mathematical model so as to be able toreduce the big M constant. To this end, the rule defines a procurementlot size, which is greater than 1. If, for example, one million items ofa product are to be procured, the value of the procurement variablewould be 1.000.000 without application of the fifth rule. On the otherhand, if a lot size of, e.g., 1.000 items is defined in accordance withthe fifth rule, the value of the procurement variable would be 1.000only since the optimizer would now work on multiples of the lot size1.000.

Exemplary Rules for Remodelling

In many cases, several alternative models exist for representing asupply chain. While the alternative models may be “equivalent” in alogical sense, there may be differences with respect to the efficiencywith which the models can be solved. Thus, one would prefer a model thatis easier to solve than others.

In accordance with another embodiment, a sixth rule and a seventh rulemay be provided that target at simplifying or reducing the problem byremodelling the same. The basic idea is as follows: If it is possible todirectly derive a dependent decision from a planning decision, thedependent decision can be removed from the model since it can always bereconstructed from the superordinate decision.

The sixth rule relates to the reduction of supplier locations.Suppliers, which may, e.g., deliver a raw material, are representeddirectly as a location in many supply chain models and are connected tothe production locations by a transport link. When optimizing the supplychain model, variables representing stock at the supplier and thetransport to the production location will then have to be provided. Inmany cases, however, the supplier's stock is always zero because theremay be no reason to build up a stock, e.g., if no capacity restrictionsare modelled for the supplier. Further, the transport to the productionlocation can always be derived from the demand and the time of demand ofthe raw product at the production location. In the mathematical model,the variables that represent the supplier location and the transportrelationship can be saved if a direct possibility of “producing” the rawproduct at the production location is modelled rather than an explicitsupplier location. The sixth rule may perform this kind ofpreprocessing.

An example of the application of the sixth rule is illustrated in FIG.5. The upper portion of FIG. 5 shows a supplier location L1, at whichproducts A, B, C are produced. The products A, B, C are transported to alocation L2 as indicated by a transport arrow 74. According to the sixthrule, the supplier location L1 can be removed if all products producedat this location can be removed. The lower portion of FIG. 5 illustratesthe situation after removal of the product A from the supplier locationL1. In the lower portion of FIG. 5, the product A is shown as being“produced” at location L2. As there is a direct relationship between theproduction of the product A at the supplier location L1, the transportof the product A and its demand at location L2, the supply chain can beremodelled by assuming that the product A is produced directly at thelocation L2. In the example shown in FIG. 5, the same direct dependencybetween the procurement at location L1 and the demand at location L2also exists for the products B and C. Accordingly, the supplier locationL1 can be entirely removed and also the transport connection 74 can beremoved from the supply chain model.

The seventh rule relates to the reduction of customer locations. As withsuppliers, many supply chain models represent customers using explicitcustomer locations. Again, stock at the customer and the transport ofthe products to the customer must be modelled at the mathematical level.In a case where there is a single location only from which a customer isprovided with a certain product, it is more efficient to propagate thecustomer demand to this location and remove the customer location alongwith the transport connection. It is this kind of preprocessing that maybe achieved by the seventh rule.

An example of the application of the seventh rule is illustrated in FIG.6. The upper portion of FIG. 6 shows a scenario where products A, B, Care delivered from a location L1 via a transport path 76 to a customerlocation L2 to satisfy a corresponding demand. If the demand for, say,product A is exclusively satisfied from the location L1, this demand canbe back-propagated from the customer location L2 to the providinglocation L1. Product A can then be eliminated at the customer locationL2. This scenario is illustrated in the lower portion of FIG. 6. Ifevery demand at the customer location L2 is satisfied by a respectivesingle previous location, all demands can be back-propagated as is shownin FIG. 6 and the entire customer location L2 can be removed.

As will be appreciated, the above explained remodelling rules allow tosimplify the core model of the supply chain planning problem and enhancethe performance of the optimizer at the mathematical level.

The computational aspects described herein can be implemented in digitalelectronic circuitry, or in computer hardware, firmware; software, or inany combination thereof. Where appropriate, aspects of these systems andtechniques can be implemented in a computer program product tangiblyembodied in a machine-readable storage device for execution by aprogrammable processor, and method steps can be performed by aprogrammable processor executing a program of instructions to performfunctions by operating on input data and generating output.

Embodiments of the invention may also be implemented in an article ofmanufacture with a computer usable medium having computer readableinstructions embodied therein for providing access to resourcesavailable on that computer, the computer readable instructionscomprising instructions to cause the computer to perform any part orsteps of methods according to the invention. Embodiments of theinvention may also be implemented as a computer program for running on acomputer system, at least including code portions for performing stepsof methods according to the invention when run on a computer system orenabling a general propose computer system to perform functions of afilter device consistent with embodiments of the invention. Such acomputer program may be provided on a data carrier, such as a CD-ROM ordiskette, stored with data loadable in a memory of a computer system,the data representing the computer program. The data carrier may furtherinclude a data connection, such as a telephone cable or a wirelessconnection transmitting signals representing a computer programaccording to the invention.

While the invention has been described with reference to specificembodiments, those skilled in the art will understand that variouschanges may be made and equivalents may be substituted without departingfrom the scope of the invention. For instance, one or more of the stepsof the disclosed methods may be deleted, rearranged, substituted orotherwise modified. In addition, many modifications may be made to adapta particular step or structure to the teachings of the invention withoutdeparting from its scope.

1. A computer-implemented system architecture for performing supplychain planning, the system comprising: a database storing master datadescriptive of supply chain items; a model generator coupled to thedatabase and configured to derive a master data-based core modelrepresentative of a supply chain planning problem; a solver configuredto translate the core model into a mathematical model and determine asolution to the mathematical model; and a preprocessor configured topreprocess the core model by subjecting the core model to a set of rulesto derive a preprocessed core model, wherein the solver establishes themathematical model from the preprocessed core model.
 2. The system ofclaim 1, wherein the set of rules include one or more redundancyelimination rules.
 3. The system of claim 1, wherein the set of rulesinclude one or more remodelling rules.
 4. The system of claim 1, whereinthe set of rules include one or more big number reduction rules.
 5. Thesystem of claim 1, wherein the set of rules include one or more boundreduction rules.
 6. A computer-implemented method for performing supplychain planning, the method comprising: storing, in a database, masterdata descriptive of supply chain items; deriving, with a model generatorcoupled to the database, a master data-based core model representativeof a supply chain planning problem; translating the core model into amathematical model and determining a solution to the mathematical model;and preprocessing the core model by subjecting the core model to a setof rules to derive a preprocessed core model, wherein the mathematicalmodel is established from the preprocessed core model.
 7. The method ofclaim 6, wherein the set of rules include one or more redundancyelimination rules.
 8. The method of claim 6, wherein the set of rulesinclude one or more remodelling rules.
 9. The method of claim 6, whereinthe set of rules include one or more big number reduction rules.
 10. Themethod of claim 6, wherein the set of rules include one or more boundreduction rules.
 11. A computer readable medium comprising programinstructions for causing a processor to perform a method of supply chainplanning, the method comprising: storing master data descriptive ofsupply chain items; deriving, based on the stored master data, a masterdata-based core model representative of a supply chain planning problem;translating the core model into a mathematical model and determining asolution to the mathematical model; and preprocessing the core model bysubjecting the core model to a set of rules to derive a preprocessedcore model, wherein the mathematical model is established from thepreprocessed core model.
 12. The computer readable medium of claim 11,wherein the set of rules include one or more redundancy eliminationrules.
 13. The computer readable medium of claim 11, wherein the set ofrules include one or more remodelling rules.
 14. The computer readablemedium of claim 11, wherein the set of rules include one or more bignumber reduction rules.
 15. The computer readable medium of claim 11,wherein the set of rules include one or more bound reduction rules.